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5.9 References and Further Reading

The implementations of the elementary and trigonometric functions are based on the following papers,

• T. E. Hull, Thomas F. Fairgrieve, Ping Tak Peter Tang, “Implementing Complex Elementary Functions Using Exception Handling”, ACM Transactions on Mathematical Software, Volume 20 (1994), pp 215--244, Corrigenda, p553
• T. E. Hull, Thomas F. Fairgrieve, Ping Tak Peter Tang, “Implementing the complex arcsin and arccosine functions using exception handling”, ACM Transactions on Mathematical Software, Volume 23 (1997) pp 299--335

The general formulas and details of branch cuts can be found in the following books,

• Abramowitz and Stegun, Handbook of Mathematical Functions, “Circular Functions in Terms of Real and Imaginary Parts”, Formulas 4.3.55--58, “Inverse Circular Functions in Terms of Real and Imaginary Parts”, Formulas 4.4.37--39, “Hyperbolic Functions in Terms of Real and Imaginary Parts”, Formulas 4.5.49--52, “Inverse Hyperbolic Functions--relation to Inverse Circular Functions”, Formulas 4.6.14--19.
• Dave Gillespie, Calc Manual, Free Software Foundation, ISBN 1-882114-18-3